Study on Solid–Liquid Phase Change Heat Transfer in Three-Dimensional Fractal Porous Media Using the Lattice Boltzmann Method

Phase change materials (PCMs) represent promising functional media for thermal energy storage and thermal management applications, particularly in battery thermal management systems. Although fractal porous skeletons are capable of substantially boosting the heat transfer performance of composite PCMs, the underlying mechanisms governing mushy zone evolution and coupled heat and mass transport during solid–liquid phase change within fractal porous media have not been fully elucidated. In the present study, a three-dimensional, pore-scale, two-region multiphase flow mathematical model is developed within the lattice Boltzmann method (LBM) framework. Three-dimensional numerical simulations are carried out to resolve the solid–liquid melting process in a three-dimensional cubic cavity embedded with fractal porous media. The combined effects of the Rayleigh number (Ra), Prandtl number (Pr), and pore fractal dimension (Ds) on mushy zone dynamics and coupled flow and heat transfer characteristics are systematically explored. This work provides mechanistic insights into mushy zone evolution for solid–liquid phase change confined by fractal porous skeletons and offers theoretical guidance for the rational design of porous composite PCMs targeting phase change energy storage and battery thermal management implementations. Quantitatively, increasing Ra from 104 to 106 reduces the dimensionless complete melting time from 0.215 to 0.143, and increasing Pr from 0.1 to 10 reduces it from 0.224 to 0.138. In addition, a smaller pore fractal dimension (Ds) accelerates melting through a higher effective thermal conductivity despite a stronger suppression of natural convection. The model is validated against a classical melting benchmark (maximum deviation 3.8%), a pure conduction case (0.7%), and a pore-resolved permeability test (within 7%). Additional numerical simulations conducted under conditions of fixed porosity confirmed that this acceleration effect is jointly driven by the effective thermal conductivity of the skeleton and pore fractal dimension (Ds).